## mahela007 Group Title Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session.. 3 years ago 3 years ago

Differentiation is defined by a limit, and limits need not always exist. If the limit $\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}$ exists at a particular x value then we say the function is differentiable at that point. It it exists for all x in an interval then it is differentiable on that interval. Note that the limit is double sided, so implicit in this definition is the fact that no function defined on a closed interval can be differentiable on that closed interval, thus why the wording of many of the basic theorems insist on certain intervals being open...